Covariant algebraic Reynolds stress modelling of curvature effects in high-Reynolds-number Taylor--Couette turbulence
Nearly constant mean angular momentum profiles are widely observed in curved turbulent flows, including the bulk region of Taylor--Couette (TC) flows, where the inner and outer cylinders have weakly counter-rotating and co-rotating conditions. For high-Reynolds-number TC flows under these conditions...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
12.09.2024
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Subjects | |
Online Access | Get full text |
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Summary: | Nearly constant mean angular momentum profiles are widely observed in curved
turbulent flows, including the bulk region of Taylor--Couette (TC) flows, where
the inner and outer cylinders have weakly counter-rotating and co-rotating
conditions. For high-Reynolds-number TC flows under these conditions, both the
bulk and boundary layers become turbulent without Taylor rolls, referred to as
the featureless ultimate regime (UR). In this study, we examine
Reynolds-averaged Navier--Stokes (RANS) models to predict the nearly constant
mean angular velocity as a one-dimensional problem in the featureless UR of TC
turbulence. High-Reynolds-number experiments of TC turbulence are performed for
reference, where the radius ratio is $\eta = r_\mathrm{in}/r_\mathrm{out} =
0.732$ and angular velocity ratio $a = -\omega_\mathrm{out}/\omega_\mathrm{in}$
is in the range $-0.5 \le a \le 0.1$. Verification of the RANS model using the
algebraic Reynolds stress model (ARSM) suggests that convection of the Reynolds
stress is essential for predicting the angular momentum profile. We introduce
the Jaumann derivative as a covariant time derivative to develop ARSMs that
incorporate the convection effect in a covariant manner. The proposed ARSM
using the Jaumann derivative of the term composed of the strain and vorticity
tensors successfully predicts the nearly constant mean angular momentum for a
wide range of angular velocity ratios in the co-rotating case. The modelling
approach incorporating time-derivative terms is a candidate for expressing
curvature effects while satisfying the covariance of the Reynolds stress
tensor. |
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DOI: | 10.48550/arxiv.2409.08471 |